Problem: Given $ m \angle MON = 9x - 1$, and $ m \angle LOM = 7x - 107$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {7x - 107} + {9x - 1} = {180}$ Combine like terms: $ 16x - 108 = 180$ Add $108$ to both sides: $ 16x = 288$ Divide both sides by $16$ to find $x$ $ x = 18$ Substitute $18$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 9({18}) - 1$ Simplify: $ {m\angle MON = 162 - 1}$ So ${m\angle MON = 161}$.